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Simplifying 3x4 + 12x2 + -18 = 0 Reorder the terms: -18 + 12x2 + 3x4 = 0 Solving -18 + 12x2 + 3x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-6 + 4x2 + x4) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-6 + 4x2 + x4)' equal to zero and attempt to solve: Simplifying -6 + 4x2 + x4 = 0 Solving -6 + 4x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 4x2 + 6 + x4 = 0 + 6 Reorder the terms: -6 + 6 + 4x2 + x4 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 4x2 + x4 = 0 + 6 4x2 + x4 = 0 + 6 Combine like terms: 0 + 6 = 6 4x2 + x4 = 6 The x term is 4x2. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x2 + 4 + x4 = 6 + 4 Reorder the terms: 4 + 4x2 + x4 = 6 + 4 Combine like terms: 6 + 4 = 10 4 + 4x2 + x4 = 10 Factor a perfect square on the left side: (x2 + 2)(x2 + 2) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (x2 + 2) equal to 3.16227766 and -3.16227766.Subproblem 1
x2 + 2 = 3.16227766 Simplifying x2 + 2 = 3.16227766 Reorder the terms: 2 + x2 = 3.16227766 Solving 2 + x2 = 3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x2 = 3.16227766 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = 3.16227766 + -2 x2 = 3.16227766 + -2 Combine like terms: 3.16227766 + -2 = 1.16227766 x2 = 1.16227766 Simplifying x2 = 1.16227766 Take the square root of each side: x = {-1.07808982, 1.07808982}Subproblem 2
x2 + 2 = -3.16227766 Simplifying x2 + 2 = -3.16227766 Reorder the terms: 2 + x2 = -3.16227766 Solving 2 + x2 = -3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x2 = -3.16227766 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = -3.16227766 + -2 x2 = -3.16227766 + -2 Combine like terms: -3.16227766 + -2 = -5.16227766 x2 = -5.16227766 Simplifying x2 = -5.16227766 Reorder the terms: 5.16227766 + x2 = -5.16227766 + 5.16227766 Combine like terms: -5.16227766 + 5.16227766 = 0.00000000 5.16227766 + x2 = 0.00000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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